Naples is the birthplace of pizza, but most tourists never get further south than Rome – so if you’re going to try pizza in Italy and you’re not heading to Naples, Rome is your best bet. Check out this video for an example of one pizzeria in Rome:
You may have noticed that the patrons were eating their pizzas with a knife and fork, not picking up slices (well, except for the hostess of the video who ate a slice at the end, but she’s not Italian so I can’t blame her). Italians order pizzas as personal meals, not as something to share, and they arrive in one piece. Then, they’re eaten with a knife and fork, one bite at a time. If you do want to cut your pizza into slices, American-style, you can – but the “proper” way to eat slices in Italy is by folding them in half, length-wise, before starting to bite into them.
Personally, I eat pizzas in Italy come gli italiani – as the Italians do – with a knife and fork. I have a tendency to eat the entire middle and leave the crust behind because the crust would fill me up too quickly and I wouldn’t have room for the goodies on the inside, but you can do as you wish. Be warned that I did once have a waiter at a pizzeria ask me if I had a problem with the crust when I left it behind – he seemed offended.